2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192667Inspired by the renormalizability of the non-commutative Phi^4 model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.7 pages; v2 revised, v3 corrected eq. (14) and related text, references updatedHigh Energy Physics - Theorytext